1. Field of the Invention
The present invention pertains to means and methods for processing digital signals, and more particularly, it pertains to digital techniques or digital processors, such as digital filters or other spectral resolution devices, which digitally compute the Fourier transform of a sequence of digital data signals.
2. Description of the Prior Art
In the design of distal filters or other digital devices requiring spectral resolution (e.g., spectral ratio measuring devices to determine the attenuation coefficient or quality factor from seismic and acoustic dam), a commonly used technique is the discrete Fourier transform (DFT) or the fast Fourier Waveform (FFT) wherein a sequence of digital data readings or train of digital signals, in the time domain is transformed into the frequency domain for a selective elimination (digital filtering) or ratio measurement (attenuation coefficient or Q factor measuring). A continuing problem with such methods is the well known Gibbs phenomenon which appears in a discrete Fourier transform due to the incomplete DFT periodicity of the arbitrary sequence of digital data that is a sequence started at an arbitrary point in time. That is to say, the start and end values in the digital data sequence provide discontinuities which introduce spurious frequency components into the Fourier transformed data or distort the frequency components which are already present. The conventional way to treat the Gibbs phenomenon is to apply a window function to the data sequence to taper the data to zero at the end points. However, the use of the conventional windowing technique may distort the frequency components to be measured or induce spectral leakage, i.e., the introduction of spurious frequency components.